Rates of change and differential equations.
Connect implicit and time derivatives to differential equations, slope fields, growth and one-dimensional motion.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Implicit differentiation
Differentiate a relation containing both x and y, and use its derivative to describe a tangent.
- 02
Related-rate problems
Connect changing quantities through a geometric relation and differentiate with respect to time.
- 03
Differential equations and initial conditions
Interpret a differential equation, verify a proposed solution and use initial data to choose one member of a family.
- 04
Slope fields
Read local directions from a differential equation and sketch solution curves through specified starting points.
- 05
Direct integration
Recover a changing quantity by integrating its known derivative and applying initial information.
- 06
Separation of variables
Solve separable differential equations while retaining equilibrium solutions and domain restrictions.
- 07
Exponential and logistic models
Use exponential and logistic models to connect rates, initial values, limiting behaviour and model assumptions.
- 08
Interpreting motion equations and simple harmonic motion
Interpret one-dimensional motion equations and recognise simple harmonic motion from its differential equation.
Topic review
Revisit the key ideas, then choose a practice paper.